The weak elliptic Harnack inequality revisited

In this paper we firstly derive the weak elliptic Harnack inequality from the generalized capacity condition, the tail estimate of jump measure and the Poincar\'{e} inequality, for any regular Dirichlet form without killing part on a measure metric space, by using the lemma of growth and the Jo...

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Bibliographic Details
Published in:arXiv.org 2022-08
Main Authors: Hu, Jiaxin, Yu, Zhenyu
Format: Article
Language:English
Subjects:
Dirichlet problem
Metric space
Online Access:Get full text
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Summary:In this paper we firstly derive the weak elliptic Harnack inequality from the generalized capacity condition, the tail estimate of jump measure and the Poincar\'{e} inequality, for any regular Dirichlet form without killing part on a measure metric space, by using the lemma of growth and the John-Nirenberg inequality. We secondly show several equivalent characterizations of the weak elliptic Harnack inequality for any (not necessarily regular) Dirichlet form. We thirdly present some consequences of the weak elliptic Harnack inequality.
ISSN:2331-8422